PercentagesPercentages

Objectives:D Grade Increase or decrease a quantity by a given

percentage

C Grade Work out a percentage increase or decrease

Prior knowledge:

Understand :

Finding percentages of quantities – calculator and non calculator

Use of percentage multipliers to find the percentage of a quantity

Percent to decimal conversion (i.e. percent ÷ 100)

PercentagesPercentages

Percentage increase

Find the percentage of the quantity and add it to the original

Example 1:

Increase 200 by 12% 12 × 200100

2= 24

cancel common factors 200 + 24 = 224

Example 2:

Increase 270 by 40%

cancel common factors 270 + 108 = 378

40 × 270100

4

10≡ = 108

PercentagesPercentages

Percentage decrease

Find the percentage of the quantity and subtract it from the original

Example 1:

Decrease 200 by 12% 12 × 200100

2= 24

cancel common factors 200 - 24 = 176

Example 2:

Decrease 270 by 40%

cancel common factors 270 - 108 = 162

40 × 270100

4

10≡ = 108

PercentagesPercentagesNow do these:

1. Increase 250 by 10%

2. Decrease 500 by 6%

3. Decrease 24 by 25%

4. Increase 80 by 30%

5. Increase £4.20 by 15%

275

470

18

104

£4.83

PercentagesPercentages

Percentage increase

When calculating a percentage increase of a quantity we are starting with 100% and then we add the percentage asked for.

e.g. Increase a quantity by 23%

100 % + 23 % = 123 %

100 % + 23 % = 123 %

In order to do this calculation we write the percent as a fraction in hundredths. So this becomes:

100 + 23 = 123100 100 100

Now 123 = 1.23 100

This is called the percentage multiplier for a percentage increase

PercentagesPercentages

Example :

Increase 345 by 56%

the percentage multiplier is 1.56

100 % + 56 % = 156 % 156 = 1.56100

345 × 1.56 = 538.2

PercentagesPercentagesNow do these:

1. Increase 125 by 16%

2. Increase 340 by 9%

3. Increase 575 by 22%

4. Increase 84 by 1.3%

5. Increase £6.30 by 17.5%

Percentage multiplier is 1.16125 × 1.16 = 145

Percentage multiplier is 1.09340 × 1.09 = 370.6

Percentage multiplier is 1.22575 × 1.22 = 701.5

Percentage multiplier is 1.01380 × 1.013 = 81.04

Percentage multiplier is 1.1756.30 × 1.175 = £7.40

PercentagesPercentages

Percentage decrease

When calculating a percentage decrease of a quantity we are starting with 100% and then we subtract the percentage asked for.e.g. decrease a quantity by 23%

100 % - 23 % = 77 %

100 % - 23 % = 77 %

In order to do this calculation we write the percent as a fraction in hundredths. So this becomes:

100 - 23 = 77100 100 100

Now 77 = 0.77 100

This is called the percentage multiplier for a percentage decrease

PercentagesPercentages

Example :

Decrease 345 by 56%

the percentage multiplier is 0.44

100 % - 56 % = 44 % 44 = 0.44100

345 × 0.44 = 151.8

PercentagesPercentagesNow do these:

1. Decrease 137 by 13%

2. Decrease 78 by 6%

3. Decrease 623 by 37%

4. Decrease 467 by 1.3%

5. Decrease £7.45 by 17.5%

Percentage multiplier is 0.87137 × 0.87 = 119.19

Percentage multiplier is 0.9478 × 0.94 = 73.32

Percentage multiplier is 0.63623 × 0.63 = 392.49

Percentage multiplier is 0.987467 × 0.987 = 460.929

Percentage multiplier is 0.8257.45 × 0.825 = £6.15

PercentagesPercentages

To summarise percentage calculations

Original quantity × percentage multiplier = new quantity

By understanding how to rearrange equations you can find any of the three if you know the other two.

PercentagesPercentagesWorksheet 1

Mixed Non-Calculator

1. Todd is paid £350 per week. He gets a 4% pay rise.What is his new weekly pay?

2. A package holiday is priced at £660. Julie gets a 10% discount for booking before the end of January. How much does she

pay?

3. Chris has 50 books on his shelves. Jenny has 12% more books.How many books has Jenny got?

4. A train ticket is priced at £48. In the new year the cost increases by 2½ %. What is the new cost of the train ticket?

5. A music centre costs £280. VAT is added at 17 ½ %. What is

the total cost

£364

£594

£56

£49.20

£329

PercentagesPercentagesWorksheet 2

Mixed Calculator1. Sarah’s salary is £13 575 per year. Her annual bonus is 1¾% of

her salary. How much does she earn altogether?

2. Jack sells computers. He is paid commission of 8¼% on his sales. Last year he sold computers worth £85 496.

How much was his commission?

3. Nathan buys a new Fiat for £12 499. Over 2 years it depreciates

by 45%. What is the value after 2 years

4. The population of Newtown was 74 970 in 2008. By 2009 the population had decreased by 27%. What is the population in

2009.

5. Decrease £9.55 by 12%

£13 812.56

£7 053.42

£6 874.45

54 728

£7.40

PercentagesPercentagesWorksheet 1

Mixed Non-Calculator

1. Todd is paid £350 per week. He gets a 4% pay rise.What is his new weekly pay?

2. A package holiday is priced at £660. Julie gets a 10% discount for booking before the end of January. How much does she

pay?

3. Chris has 50 books on his shelves. Jenny has 12% more books.How many books has Jenny got?

4. A train ticket is priced at £48. In the new year the cost increases by 2½ %. What is the new cost of the train ticket?

5. A music centre costs £280. VAT is added at 17 ½ %. What is

the total cost

PercentagesPercentagesWorksheet 2

Mixed Calculator1. Sarah’s salary is £13 575 per year. Her annual bonus is 1¾% of

her salary. How much does she earn altogether?

2. Jack sells computers. He is paid commission of 8¼% on his sales. Last year he sold computers worth £85 496.

How much was his commission?

3. Nathan buys a new Fiat for £12 499. Over 2 years it depreciates

by 45%. What is the value after 2 years

4. The population of Newtown was 74 970 in 2008. By 2009 the population had decreased by 27%. What is the population in

2009.

5. Decrease £9.55 by 12%